Many high temperature superconducting (HTS) tape manufactures make an effort to reduce the transport current loss of HTS tapes. The knowledge of critical current and self-field in an HTS tape is very useful to compute the transport current losses. The spatial distribution and magnitude of self-field are variable due to the neighboring materials. In this paper, the critical currents and the transport current losses of BSCCO and YBCO tapes with paralleled magnetic material (Ni tape) and/or diamagnetic material (BSCCO tape) are experimentally investigated to improve the AC loss properties. The critical currents of HTS tapes with paralleled Ni tape are slightly decreased and the transport current losses are markedly increased. However, the critical currents and transport current losses of HTS tapes with paralleled BSCCO tape have not current carrying are more improved than single HTS tape.